Use 3D mouse in Blender
I've gotten about 3/4 of the way there on this. I can move in every axis. However, you have to hold shift to Pan. While panning, you can't orbit. It's quite frustrating, but it's better than nothing, I suppose. Do the following:

Reverse all axes and crank them up to max in the 3DConnexion software.

I have the following settings in Blender: